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Division of the 5/1 into 17 tones


A hyperpyth tuning, 17ed5 offers a good compromise between 13/5 and 17/5, but the 9/5 of 983 cents is a little bit flat. However, in hyperpyth, 21/5 isn't necessarily represented, at least not as well. In 17ed5, the 21/5 is represented about as well as the 9/5 is, although that's not too good. Luckily, 27, 29, and 39 do a fair job of it. Nevertheless it's the simplest equal hyperpyth after 5ed5, and quite consonant. I imagine it to be the traditional tonality of the tiny creatures living on subatomic particles.

But wait, an interesting pattern emerges:

22ed5 focuses on 9/5
27ed5 focuses on 13/5
29ed5 focuses on 17/5
(and 34=17*2)

so: 22+27+29=78=39*2
and behold, of the lot, 39ed5 offers the best balance between those intervals.

0: 0.000 cents
1/1

1: 163.901


2: 327.802


3: 491.702


4: 655.603


5: 819.504


6: 983.405
9/5, 16/9, 7/4
1017
7: 1147.306


8: 1311.206


9: 1475.107


10: 1639.008
13/5
1654
11: 1802.909


12: 1966.810


13: 2130.710
17/5
2118
14: 2294.611


15: 2458.512
(21/5)
2486
16: 2622.413


17: 2786.314
5/1